I always found it confusing that the lithium solution is most of the mass of the battery but all of the energy is in the anode and cathode.
The anode and cathode need to be electrically insulated from one another requiring a substantial gap, or else the battery will short out internally or self-discharge if the electrical resistance is too low. That's why it's so big. Of course, reducing that gap is a big area of research. Solid electrolytes in principle might be easier to do this with since they stay put, but stuff cracks when lithium concentrations go up and down. The materials literally swell with lithium at the nanometer scale and then break apart. It's pretty hard, you can't unfortunately just vapor deposit a thin film of a solid electrolyte on the cathode since the materials are a bit too fragile to maintain the electrical resistance required for it to work.